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Simplifying 2n2 + -5n + -4 = 6 Reorder the terms: -4 + -5n + 2n2 = 6 Solving -4 + -5n + 2n2 = 6 Solving for variable 'n'. Reorder the terms: -4 + -6 + -5n + 2n2 = 6 + -6 Combine like terms: -4 + -6 = -10 -10 + -5n + 2n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -10 + -5n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -2.5n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.5n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -2.5n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.5n + n2 = 0 + 5 -2.5n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.5n + n2 = 5 The n term is -2.5n. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5n + 1.5625 + n2 = 5 + 1.5625 Reorder the terms: 1.5625 + -2.5n + n2 = 5 + 1.5625 Combine like terms: 5 + 1.5625 = 6.5625 1.5625 + -2.5n + n2 = 6.5625 Factor a perfect square on the left side: (n + -1.25)(n + -1.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (n + -1.25) equal to 2.561737691 and -2.561737691.Subproblem 1
n + -1.25 = 2.561737691 Simplifying n + -1.25 = 2.561737691 Reorder the terms: -1.25 + n = 2.561737691 Solving -1.25 + n = 2.561737691 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + n = 2.561737691 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + n = 2.561737691 + 1.25 n = 2.561737691 + 1.25 Combine like terms: 2.561737691 + 1.25 = 3.811737691 n = 3.811737691 Simplifying n = 3.811737691Subproblem 2
n + -1.25 = -2.561737691 Simplifying n + -1.25 = -2.561737691 Reorder the terms: -1.25 + n = -2.561737691 Solving -1.25 + n = -2.561737691 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + n = -2.561737691 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + n = -2.561737691 + 1.25 n = -2.561737691 + 1.25 Combine like terms: -2.561737691 + 1.25 = -1.311737691 n = -1.311737691 Simplifying n = -1.311737691Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.811737691, -1.311737691}
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